The minimum aperture specified is not a brightness requirement, it's a geometry requirement, as it is a function of the distance between the measuring points on the AF array.

That’s what I expected, and I was concerned that the phase detection system would need an aperture of at least F5.6 to make its comparison. I remember one or the other half of the split screen in my Pentax manual focus viewfinder being blacked out with a 2X teleconverter on my F4 telephoto zoom. I’m delighted to have confirmation that my D90 should autofocus OK with the Sigma lens.